Related papers: Complexity Bounds on Quantum Search Algorithms in …
We consider the quantum search problem with a continuous time quantum walk for networks of finite spectral dimension d_{s} of the network Laplacian. For general networks of fractal (integer or non-integer) dimension d_{f}, for which in…
One of the significant breakthroughs in quantum computation is Grover's algorithm for unsorted database search. Recently, the applications of Grover's algorithm to solve global optimization problems have been demonstrated, where unknown…
We consider discrete-time evolution equations in which the stochastic operator of a classical random walk is replaced by a unitary operator. Such a problem has gained much attention as a framework for coined quantum walks that are essential…
Searching a database is a central task in computer science and is paradigmatic of transport and optimization problems in physics. For an unstructured search, Grover's algorithm predicts a quadratic speedup, with the search time…
We recast Grover's generalised search algorithm in a geometric language even when the states are not approximately orthogonal. We provide a possible search algorithm based on an arbitrary unitary transformation which can speed up the steps…
Quantum algorithms for searching one or more marked items on a d-dimensional lattice provide an extension of Grover's search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms…
With the growing interest in quantum machine learning, the perceptron -- a fundamental building block in traditional machine learning -- has emerged as a valuable model for exploring quantum advantages. Two quantum perceptron algorithms…
Grover's algorithm provides a quadratic speedup over classical algorithms for searching unstructured databases and is known to be strictly optimal in oracle query complexity, with tight bounds on its success probability. Although the…
In the emerging domain of quantum algorithms, the Grover's quantum search is certainly one of the most significant. It is relatively simple, performs a useful task and more importantly, does it in an optimal way. However, due to the success…
Spatial search on graphs is one of the most important algorithmic applications of quantum walks. To show that a quantum-walk-based search is more efficient than a random-walk-based search is a difficult problem, which has been addressed in…
Grover's quantum search algorithm can be formulated as a quantum particle randomly walking on the (highly symmetric) complete graph, with one vertex marked by a nonzero potential. From an initial equal superposition, the state evolves in a…
In this paper, we study Grover's search algorithm focusing on continuous-time quantum walk on graphs. We propose an alternative optimization approach to Grover's algorithm on graphs that can be summarized as follows: instead of finding…
A quantum walk on a lattice is a paradigm of a quantum search in a database. The database qubit strings are the lattice sites, qubit rotations are tunneling events, and the target site is tagged by an energy shift. For quantum walks on a…
Search-base algorithms have widespread applications in different scenarios. Grover's quantum search algorithms and its generalization, amplitude amplification, provide a quadratic speedup over classical search algorithms for unstructured…
Given a parameterized quantum circuit such that a certain setting of these real-valued parameters corresponds to Grover's celebrated search algorithm, can a variational algorithm recover these settings and hence learn Grover's algorithm? We…
Quantum advantage is the core of quantum computing. Grover's search algorithm is the only quantum algorithm with proven advantage to any possible classical search algorithm. However, realizing this quantum advantage in practice is quite…
The main approach to hybrid quantum-classical neural networks (QNN) is employing quantum computing to build a neural network (NN) that has quantum features, which is then optimized classically. Here, we propose a different strategy: to use…
A quantum computer encodes information in quantum states and runs quantum algorithms to surpass the classical counterparts by exploiting quantum superposition and quantum correlation. Grover's quantum search algorithm is a typical quantum…
We study spatial search with continuous-time quantum walks on real-world complex networks. We use smaller replicas of the Internet network obtained with a recent geometric renormalization method introduced by Garc\'ia-P\'erez et al., Nat.…
Random walks describe diffusion processes, where movement at every time step is restricted to only the neighbouring locations. We construct a quantum random walk algorithm, based on discretisation of the Dirac evolution operator inspired by…